LTV curve

Also called: LTV, lifetime value, customer lifetime value, CLV, CLTV

Cumulative revenue (or gross profit) per user of a cohort by day or month since joining. Its shape shows when a cohort pays back and whether it's still growing.

LTV (lifetime value) is how much money an acquired user brings over their whole life with the product. For decisions about marketing spend, count it as gross profit, not revenue: what's left after the app stores' commission, payment fees and the direct cost of serving the user. And always say per whom: per installed user, per signed-up user or per paying customer. These are different numbers.

The honest way to calculate it is the LTV curve. Take one cohort (everyone who joined in the same week or month), add up everything that cohort paid by each day or month since joining, and divide by the size of the cohort:

$\text{LTV}_t = \frac{\text{cumulative gross profit from the cohort up to age } t}{\text{number of users in the cohort}}$

The curve rises steeply at first (trials convert, first payments arrive) and then flattens as users churn. Its shape answers practical questions: by which month does a cohort cover its acquisition cost, is it still climbing, do newer cohorts sit above or below older ones. To estimate LTV beyond the data you have, extrapolate the tail with the decline you actually observe, and stop at a fixed horizon (12 or 24 months) instead of assuming users stay forever.

The textbook shortcut is

$\text{LTV} \approx \frac{\text{ARPU} \times \text{gross margin}}{\text{monthly churn}}$

It assumes churn is the same every month. It never is: churn is highest right after signup and much lower among users who stayed. Put in early churn and the formula understates LTV; put in the churn of long-time subscribers and it overstates it, sometimes several times over. It also blends cohorts and plans (a yearly plan pays twelve months at once). Use the shortcut for a sanity check on a mature, stable subscription base, and the cohort curve for anything you'll spend money on.

Example

Halves looks at the March cohort: 2,000 new users. Halves keeps 80% of subscription revenue as gross profit (after the store commission and server costs).

Month	Revenue	Gross profit (80%)	Cumulative GP	LTV per user
1	$1,400	$1,120	$1,120	$0.56
2	$900	$720	$1,840	$0.92
3	$700	$560	$2,400	$1.20
4	$600	$480	$2,880	$1.44
5	$550	$440	$3,320	$1.66
6	$520	$416	$3,736	$1.87

By month 6 each March user has brought $1.87 of gross profit, and the curve is still rising slowly: monthly gross profit fell from $440 to $416, a decline of about 5.5%. Extending that decline to month 12 adds 416 × 0.945 + 416 × 0.945² + … + 416 × 0.945⁶ ≈ $2,057, so the 12-month LTV is (3,736 + 2,057) ÷ 2,000 ≈ $2.90 per user.

Now the shortcut. Month-1 ARPU is $1,400 ÷ 2,000 = $0.70, so gross profit per user is $0.56. With the 55% of users who dropped out after month 1 as churn: $0.56 ÷ 0.55 ≈ $1.02, already beaten by the real curve in month 3. With the 5.5% decline seen in month 6: $0.56 ÷ 0.055 ≈ $10.18, three and a half times the 12-month estimate. Same data, two "LTVs" ten times apart.

Common mistakes

Revenue instead of gross profit. Compare LTV with CAC only after the store commission, refunds and serving costs.
Mixed denominators. LTV per paying customer against CAC per install makes every channel look profitable.
Constant churn in the formula. ARPU ÷ churn swings wildly depending on which month's churn you plug in; read the cohort curve instead.
Extrapolating a young cohort forever. Project the observed tail to a fixed horizon and re-check the forecast as the cohort ages.
One LTV for everyone. Cohorts from different channels, seasons, platforms and prices have different curves; a blended LTV hides the ones that lose money.